Ever since the 1995 reintroduction of the gray wolf to Yellowstone National Park and central Idaho, ranchers in the region have loudly complained that their herds end up paying a heavy cost. Lately, as a result, they've taken to trapping and shooting wolves at seemingly every opportunity.

Hunters have already exterminated more than a third of the 1,600 wolves that were thought to live in Wyoming, Montana, and Idaho in 2012, when the U.S. Fish and Wildlife Service ended endangered species protection for gray wolves there. Environmentalists now worry about the danger of a new regional extinction. Ranchers and some state wildlife officials meanwhile seem to be ardently working to achieve it.

The wolves are no longer safe even within a protected federal wilderness: Just last week, facing a lawsuit by environmental groups, the state of Idaho recalled a hunter it had sent into the Frank Church–River of No Return National Wilderness Area to kill wolves there. Environmentalists claimed a small victory. But state officials said the hunter had already killed nine wolves and presumably eliminated the two wolf packs thought to inhabit the wilderness.

Together with his coauthors, Joseph P. Ramler, a graduate student in economics at the University of Montana, examined detailed livestock records spanning 15 years for 18 ranches in western Montana. Ranchers there typically graze cattle for part of the season on their own pastures and then, for much of the summer, turn them out onto federal forests and grasslands. Ten of the ranches had lost calves to wolf attacks, and eight hadn’t.

Calculating the loss from an attack is relatively easy, and states have programs to compensate ranchers for the direct loss. But ranchers also complain, according to Ramler and his coauthors, that “wolves decrease the average weight of calves by stressing mother cattle, increasing movement rates, or encouraging inefficient foraging behavior.” That is, the cattle have to spend a lot more time looking around for danger and a lot less with their heads down in the grass. The study set out to determine if ranchers are simply crying wolf, “or is there evidence that wolves have indirect effects on calf weight?”

First the good news: When the study mapped both the location of cattle and the movement of wolf packs, it found that simply having wolves in the vicinity had no effect on calves. But once a herd experienced an attack, the resulting “landscape of fear” distracted everyone from the business of grazing. When it came time for ranchers to sell those calves at the end of the season, they weighed on average 22 pounds less. For the typical ranch, that translated into a loss of $6,679 per year.

So shoot the wolves, right? On the contrary. While wolves may be the most visible threat to cattle, and even the most enraging one for ranchers, the study found that they explained “only a very small proportion of the change in calf weight,” according to coauthor Derek Kellenberg, an associate professor of economics at the University of Montana. Rainfall, extreme heat and cold, breed type, and above all, ranch husbandry, had the biggest effects on how well calves put on weight.

The study doesn’t make any policy recommendations. Kellenberg points out that recovery efforts for endangered species generally succeed only if they have proper funding. Recognizing the true costs of wolf reintroduction is a way to get that funding and then use it to win the support of ranchers, so they don’t automatically reach for a gun every time they see a wolf.

But fatter compensation programs aren’t the way to get there, says Lisa Upson, executive director of Keystone Conservation, a wildlife group based in Bozeman, Mont. She argues that the ranchers themselves should be working to prevent predator attacks in the first place by managing their herds more actively.

Keeping cattle safe is basically a matter of how the rancher herds them, says Matt Barnes, a former ranch manager who works for Keystone Conservation teaching ranchers how to do it. Instead of turning cattle loose to wander at large across thousands of acres of known predator habitat, range riders—that is, cowboys—stay with the cattle to watch over them and also move them into the best possible forage.

In “open herding,” the cattle stay relatively spread out, but the riders move them away from creek bottoms, and other areas where they tend to concentrate, and into upland forage. That strategy takes advantage of all the available grazing and avoids causing federal land managers to evict a herd because the creek is being hammered into dust. “Close herding,” on the other hand, involves keeping the cattle in a tighter group, sometimes with the help of temporary electric fences, and moving the herd around in a sort of rotational grazing system. In both systems, the idea is to “rekindle the herding instinct” and train cow-calf pairs to stay together. In predator habitat, there is strength in numbers.

Active management doesn’t work 100 percent of the time, Barnes says, and all the available measures cost money—typically about $2,000 a month for a range rider. So the ranching community as a whole isn’t buying into it yet. “It’s not what their fathers and grandfathers did,” says Barnes.

“But the good thing is, once you figure it out, it seems to pay for itself,” and it’s not just about avoiding both the direct and indirect costs of predator attacks. Ranchers who have experimented with more active management, says Barnes, find that they can dramatically increase the number of cattle they graze—in one case by 100 percent—and the time spent grazing. It means working closely with livestock—that is, being a rancher—but with the possibility of tens of thousands of dollars of additional income at the end of the season. Getting ranchers to buy into their own future success will, however, require transitional funding for training programs.

But that funding needs to turn up soon. Otherwise, the shooting spree will go on, and soon, the only thing wolf restoration advocates will have to show for their hard work is an empty wilderness.

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